Mathematica 9 is now available
 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Hypergeometric Related  /
LegendreQ

  • LegendreQ[ n , z ] gives the Legendre function of the second kind .
  • LegendreQ[ n , m , z ] gives the associated Legendre function of the second kind .
  • Mathematical function (see Section A.3.10).
  • For integer n and m, explicit formulas are generated.
  • The Legendre functions satisfy the differential equation .
  • LegendreQ[ n , m , a , z ] gives Legendre functions of type a. The default is type 1.
  • LegendreQ of types 1, 2 and 3 are defined in terms of LegendreP of these types, and have the same branch cut structure.
  • See the Mathematica book: Section 3.2.10.

    Further Examples

    This gives the second associated Legendre function of the second kind in the variable z.

    In[1]:=

    Out[1]=

    This gives the first associated Legendre function of the second kind.

    In[2]:=

    Out[2]=

    This is the derivative.

    In[3]:=

    Out[3]=

    This is a series expansion around .

    In[4]:=

    Out[4]=



    Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
    THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
    SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.